目錄
Preface
1 Coding for Reliable Digital Transmission and Storage
1.1 Introduction
1.2 Types of Codes
1.3 Modulation and Coding
1.4 Maximum Likelihood Decoding
1.5 Types of Errors
1.6 Error Control Strategies
1.7 Performance Measures
1.8 Coded Modulation
Bibliography
2 Introduction to Algebra
2.1 Groups
2.2 Fields
2.3 Binary Field Arithmetic
2.4 Construction of Galois Field GF (2m)
2.5 Basic Properties of a Galois Field GF (2m)
2.6 Computations Using Galois Field GF (2m) Arithmetic
2.7 Vector Spaces
2.8 Matrices
Problems
Bibliography
3 Linear Block Codes
3.1 Introduction to Linear Block Codes
3.2 Syndrome and Error Detection
3.3 The Minimum Distance of a Block Code
3.4 Error-Detecting and Error-Correcting Capabilities of a Block Code
3.5 Standard Array and Syndrome Decoding
3.6 Probability of an Undetected Error for Linear Codes over a BSC
3.7 Single-Parity-Check Codes, Repetition Codes, and Self-Dual Codes
Problems
Bibliography
4 Important Linear Block Codes
4.1 Hamming Codes
4.2 A Class of Single-Error-Correcting and Double-Error-Detecting Codes
4.3 Reed-Muller Codes
4.4 Other Constructions for Reed-Muller Codes
4.5 The Squaring Construction of Codes
4.6 The (24, 12) Golay Code
4.7 Product Codes
4.8 Interleaved Codes
Problems
Bibliography
5 Cyclic Codes
5.1 Description of Cyclic Codes
5.2 Generator and Parity-Check Matrices of Cyclic Codes
5.3 Encoding of Cyclic Codes
5.4 Syndrome Computation and Error Detection
5.5 Decoding of Cyclic Codes
5.6 Cyclic Hamming Codes
5.7 Error-Trapping Decoding
5.8 Improved Error-Trapping Decoding
5.9 The (23, 12) Golay Code
5.10 Shortened Cyclic Codes
5.11 Cyclic Product Codes
5.12 Quasi-Cyclic Codes
Problems
Bibliography
6 Binary BCH Codes
6.1 Binary Primitive BCH Codes
6.2 Decoding of BCH Codes
6.3 Iterative Algorithm for Finding the Error-Location Polynomial σ (X)
6.4 Simplified Iterative Algorithm for Finding the Error-Location Polynomial σ (X)
6.5 Finding the Error-Location Numbers and Error Correction
6.6 Correction of Errors and Erasures
6.7 Implementation of Galois Field Arithmetic
6.8 Implementation of Error Correction
6.9 Weight Distribution and Error Detection of Binary BCH Codes
6.10 Remarks
Problems
Bibliography
7 Nonbinary BCH Codes, Reed-Solomon Codes, and Decoding Algorithms
7.1 q-ary Linear Block Codes
7.2 Primitive BCH Codes over GF(q)
7.3 Reed-Solomon Codes
7.4 Decoding of Nonbinary BCH and RS Codes: The Berlekamp Algorithm
7.5 Decoding with the Euclidean Algorithm
7.6 Frequency-Domain Decoding
7.7 Correction of Errors and Erasures
Problems
Bibliography
8 Majority-Logic Decodable and Finite Geometry Codes
8.1 One-Step Majority-Logic Decoding
8.2 A Class of One-Step Majority-Logic Decodable Codes
8.3 Other One-Step Majority-Logic Decodable Codes
8.4 Multiple-Step Majority-Logic Decoding
8.5 Euclidean Geometry
8.6 Euclidean Geometry Codes
8.7 Twofold EG Codes
8.8 Projective Geometry and Projective Geometry Codes
8.9 Remarks
Problems
Bibliography
9 Trellises for Linear Block Codes
9.1 Finite-State Machine Model and Trellis Representation of a Code
9.2 Bit-Level Trellises for Binary Linear Block Codes
9.3 State Labeling
9.4 Structural Properties of Bit-Level Trellises
9.5 State Labeling and Trellis Construction Based on the Parity-Check Matrix
9.6 Trellis Complexity and Symmetry
9.7 Trellis Sectionalization and Parallel Decomposition
9.8 Low-Weight Subtrellises
9.9 Cartesian Product
Problems
Bibliography
10 Reliability-Based Soft-Decision Decoding Algorithms for Linear
Block Codes (Contributed by Marc P. C. Fossorier)
10.1 Soft-Decision Decoding
10.2 Reliability Measures and General Reliability-Based Decoding Schemes
10.3 Sufficient Conditions on the Optimality of a Decoded Codeword
10.4 Generalized Minimum Distance and Chase Decoding Algorithms
10.5 Weighted Erasure Decoding
10.6 A Maximum Likelihood Decoding Algorithm Based on Iterative Processing of the Least Reliable Positions
10.7 Reduced List Syndrome Decoding Algorithm
10.8 Most Reliable Independent Position Reprocessing Decoding Algorithms
10.9 Weighted Majority-Logic Decoding
10.10 Iterative Reliability-Based Decoding of One-Step Majority-Logic Decodable Codes
Problems
Bibliography
11 Convolutional Codes
11.1 Encoding of Convolutional Codes
11.2 Structural Properties of Convolutional Codes
11.3 Distance Properties of Convolutional Codes
Problems
Bibliography
12 Optimum Decoding of Convolntional Codes
12.1 The Viterbi Algorithm
12.2 Performance Bounds for Convolutional Codes
12.3 Construction of Good Convolutional Codes
12.4 Implementation and Performance of the Viterbi Algorithm
12.5 The Soft-Output Viterbi Algorithm (SOVA)
12.6 The BCJR algorithm
12.7 Punctured and Tail-Biting Convolutional Codes
Problems
Bibliography
13 Suboptimum Decoding of Convolutional Codes
13.1 The ZJ (Stack) Sequential Decoding Algorithm
13.2 The Fano Sequential Decoding Algorithm
13.3 Performance Characteristics of Sequential Decoding
13.4 Code Construction for Sequential Decoding
13.5 Majority-Logic Decoding
13.6 Performance Characteristics of Majority-Logic Decoding
13.7 Code Construction for Majority-Logic Decoding
Problems
Bibliography
14 Trellis-Based Soft-Decision Decoding Algorithms
14.1 The Viterbi Decoding Algorithm
14.2 A Recursive Maximum Likelihood Decoding Algorithm
14.3 A Suboptimum Iterative Decoding Algorithm Based on a Low-Weight Subtrellis
14.4 The MAP Decoding Algorithm
14.5 MAP Decoding Based on a Sectionalized Trellis
14.6 Max-log-MAP Decoding Algorithm
Problems
Bibliography
15 Concatenated Coding, Code Decomposition, and Multistage Decoding
15.1 Single-Level Concatenated Codes
15.2 Multilevel Concatenated Codes
15.3 A Soft-Decision Multistage Decoding
15.4 Decomposition of Codes
15.5 An Iterative Multistage MLD Algorithm
15.6 Concatenated Coding Schemes with Convolutional Inner Codes
15.7 Binary Concatenation
Problems
Bibliography
16 Turbo Coding
16.1 Introduction to Turbo Coding
16.2 Distance Properties of Turbo Codes
16.3 Performance Analysis of Turbo Codes
16.4 Design of Turbo Codes
16.5 Iterative Decoding of Turbo Codes
Problems
Bibliography
17 Low-Density Parity-Cheek Codes
17.1 Introduction to LDPC Codes
17.2 Tanner Graphs for Linear Block Codes
17.3 A Geometric Construction of LDPC Codes
17.4 EG-LDPC Codes
17.5 PG-LDPC Codes
17.6 Decoding of LDPC Codes
17.7 Code Construction by Column and Row Splitting
17.8 Breaking Cycles in Tanner Graphs
17.9 ShortenedFinite-Geometry LDPC Codes
1.7.10 Construction of Gallager LDPC Codes
17.11 Masked EG-Gallager LDPC Codes
17.12 Construction of Quasi-Cyclic Codes by Circulant Decomposition
17.13 Construction of LDPC Codes Based on Finite Geometries over GF(ps)
17.14 Random LDPC Codes
17.15 Irregular LDPC Codes
17.16 Graph-Theoretic LDPC Codes
17.17 Construction of LDPC Codes Based on Balanced Incomplete Block Designs
17.18 Construction of LDPC Codes Based on Shortened RS Codes with Two Information Symbols
17.19 Concatenations with LDPC and Turbo Codes
Problems
Bibliography
18 Trellis-Coded Modulation
18.1 Introduction to Trellis-Coded Modulation
18.2 TCM Code Construction
18.3 TCM Performance Analysis
18.4 Rotationally Invariant TCM
18.5 Multidimensional TCM
Problems
Bibliography
19 Block Coded Modulation
19.1 Distance Concepts
19.2 Multilevel Block Modulation Codes
19.3 Multistage Decoding of Multilevel BCM Codes
19.4 Concatenated Coded Modulation
19.5 Product Coded Modulation
19.6 Multilevel Coded Modulation for Unequal Error Protection
Problems
Bibliography
20 Burst-Error-Correcting Codes
20.1 Introduction
20.2 Decoding of Single-Burst-Error-Correcting Cyclic Codes
20.3 Single-Burst-Error-Correcting Codes
20.4 Phased-Burst-Error-Correcting Codes
20.5 Burst-and-Random-Error-Correcting Codes
Problems
Bibliography
21 Burst-Error-Correcting Convolutional Codes
21.1 Bounds on Burst-Error-Correcting Capability
21.2 Burst-Error-Correcting Convolutional Codes
21.3 Interleaved Convolutional Codes
21.4 Burst-and-Random-Error-Correcting Convolutional Codes
Problems
Bibliography
22 Automatic-Repeat-Request Strategies
22.1 BasicARQ Schemes
22.2 Selective-Repeat ARQ System with Finite Receiver Buffer
22.3 ARQ Schemes with Mixed Modes of Retransmission
22.4 Hybrid ARQ Schemes
22.5 A Class of Half-Rate Invertible Codes
22.6 Type-II Hybrid Selective-Repeat ARQ with Finite Receiver Buffer
22.7 Hybrid ARQ Systems Using Convolutional Codes
22.8 A Concatenated Coded Modulation Hybrid ARQ System
Problems
Bibliography
A Tables of Galois Fields
B Minimal Polynomials of Elements in GF (2m)
C Generator Polynomials of Binary Primitive BCH Codes of Length up to 210
Index
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